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- Schubert_calculus abstract "In mathematics, Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert, in order to solve various counting problems of projective geometry (part of enumerative geometry). It was a precursor of several more modern theories, for example characteristic classes, and in particular its algorithmic aspects are still of current interest. The objects introduced by Schubert are the Schubert cells, which are locally closed sets in a Grassmannian defined by conditions of incidence of a linear subspace in projective space with a given flag. For details see Schubert variety.The intersection theory of these cells, which can be seen as the product structure in the cohomology ring of the Grassmannian of associated cohomology classes, in principle allows the prediction of the cases where intersections of cells results in a finite set of points; which are potentially concrete answers to enumerative questions. A supporting theoretical result is that the Schubert cells (or rather, their classes) span the whole cohomology ring.In detailed calculations the combinatorial aspects enter as soon as the cells have to be indexed. Lifted from the Grassmannian, which is a homogeneous space, to the general linear group that acts on it, similar questions are involved in the Bruhat decomposition and classification of parabolic subgroups (by block matrix).Putting Schubert's system on a rigorous footing is Hilbert's fifteenth problem.".
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- Schubert_calculus wikiPageWikiLink Algebraic_geometry.
- Schubert_calculus wikiPageWikiLink American_Mathematical_Monthly.
- Schubert_calculus wikiPageWikiLink American_Mathematical_Society.
- Schubert_calculus wikiPageWikiLink Block_matrix.
- Schubert_calculus wikiPageWikiLink Borel_subgroup.
- Schubert_calculus wikiPageWikiLink Bruhat_decomposition.
- Schubert_calculus wikiPageWikiLink Category:Algebraic_geometry.
- Schubert_calculus wikiPageWikiLink Category:Topology_of_homogeneous_spaces.
- Schubert_calculus wikiPageWikiLink Characteristic_class.
- Schubert_calculus wikiPageWikiLink Cohomology.
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- Schubert_calculus wikiPageWikiLink Dan_Laksov.
- Schubert_calculus wikiPageWikiLink Enumerative_geometry.
- Schubert_calculus wikiPageWikiLink Flag_(linear_algebra).
- Schubert_calculus wikiPageWikiLink General_linear_group.
- Schubert_calculus wikiPageWikiLink Glossary_of_topology.
- Schubert_calculus wikiPageWikiLink Grassmannian.
- Schubert_calculus wikiPageWikiLink Hermann_Schubert.
- Schubert_calculus wikiPageWikiLink Hilberts_fifteenth_problem.
- Schubert_calculus wikiPageWikiLink Homogeneous_space.
- Schubert_calculus wikiPageWikiLink Incidence_(geometry).
- Schubert_calculus wikiPageWikiLink Intersection_theory.
- Schubert_calculus wikiPageWikiLink Joe_Harris_(mathematician).
- Schubert_calculus wikiPageWikiLink Locally_closed.
- Schubert_calculus wikiPageWikiLink Mathematics.
- Schubert_calculus wikiPageWikiLink Parabolic_subgroup.
- Schubert_calculus wikiPageWikiLink Phillip_Griffiths.
- Schubert_calculus wikiPageWikiLink Proceedings_of_Symposia_in_Pure_Mathematics.
- Schubert_calculus wikiPageWikiLink Projective_geometry.
- Schubert_calculus wikiPageWikiLink Schubert_variety.
- Schubert_calculus wikiPageWikiLink Steven_Kleiman.
- Schubert_calculus wikiPageWikiLinkText "Schubert calculus".
- Schubert_calculus first "Frank".
- Schubert_calculus hasPhotoCollection Schubert_calculus.
- Schubert_calculus id "S/s130080".
- Schubert_calculus last "Sottile".
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- Schubert_calculus wikiPageUsesTemplate Template:Cite_journal.
- Schubert_calculus wikiPageUsesTemplate Template:Eom.
- Schubert_calculus wikiPageUsesTemplate Template:Mergeto.
- Schubert_calculus subject Category:Algebraic_geometry.
- Schubert_calculus subject Category:Topology_of_homogeneous_spaces.
- Schubert_calculus hypernym Branch.
- Schubert_calculus type Organisation.
- Schubert_calculus type Space.
- Schubert_calculus comment "In mathematics, Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert, in order to solve various counting problems of projective geometry (part of enumerative geometry). It was a precursor of several more modern theories, for example characteristic classes, and in particular its algorithmic aspects are still of current interest.".
- Schubert_calculus label "Schubert calculus".
- Schubert_calculus sameAs m.08ny8m.
- Schubert_calculus sameAs Q7432936.
- Schubert_calculus sameAs Q7432936.
- Schubert_calculus wasDerivedFrom Schubert_calculus?oldid=621468008.
- Schubert_calculus isPrimaryTopicOf Schubert_calculus.